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Comparison of analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations

Comparison of analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations

Ďuriš, Karol, Tan, Shih-Hau, Lai, Choi-Hong ORCID: 0000-0002-7558-6398 and Ševčovič, Daniel (2016) Comparison of analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations. Computational Methods in Applied Mathematics, 16 (1). pp. 35-50. ISSN 1609-4840 (Print), 1609-9389 (Online) (doi:https://doi.org/10.1515/cmam-2015-0035)

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Abstract

Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself. In this paper, different linearization techniques such as Newton’s method and the analytic asymptotic approximation formula are adopted and compared for a wide class of nonlinear Black–Scholes equations including, in particular, the market illiquidity model and the risk-adjusted pricing model. Accuracy and time complexity of both numerical methods are compared. Furthermore, market quotes data was used to calibrate model parameters.

Item Type: Article
Uncontrolled Keywords: Nonlinear PDE, Asymptotic Formula, Newton's Method, Finite Difference Method, Option Pricing, Black–Scholes Equation
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 17 May 2019 10:45
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: GREAT 5
URI: http://gala.gre.ac.uk/id/eprint/14897

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